the transmission is one at every location except when the magnitude is

zero. When the magnitude is zero, both components are set to zero.

The Fourier transform of a test square is shown in Figure 7.2. The

same transform with high-frequency emphasized is shown in Figure 7.3.

Note in Figure 4.1 that the edges are sharply accentuated in the

modified image while broad areas are dark. Despite the modified

frequency, the image is still easily recognized. The Fourier

transform of a phase-only-filtered image has minimum dynamic range,

but the image is distorted by the extreme edge enhancement typical of

phase-only filtering. When all pre-emphasis is completed, the

reference and test patterns are normalized to possess continuous

values between 0 and 1 inclusive. Normalization is performed to

simulate the action of a transparency as would be used in an optical

correlator and allows the determination of light efficiency.

 Once the reference transform is modified according to the desired

pre-processing technique, and the point by point product taken with

the test image transform, the result is transformed again. Note that

the inverse is not taken because the lenses which are simulated can

only take forward Fourier transforms. Recall that the only difference

between a forward and inverse transform is that the result will be

inverted and perverted (see equation 2.11). It is of no consequence

in this case that the correlation is upside-down. Figures 7.4 through

7.6 show the auto-correlation of a square with no pre-emphasis,

high-frequency emphasis, and phase-only filtering applied. Note that

the correlation spikes with pre-emphasis are considerably sharper.

This is to be expected as the correlation length is inversely related

to the high-frequency content of the images.